If your Nero installation included the Nero InCD component get rid of it. It, and those of it's competitors (eg Roxio DLA), are well known to cause PRE write errors.
Did you place a Stop marker at the end of your timeline? If so remove it. The end of the timeline is automatically treated as a stop marker and adding one there can cause burn failure.
Try the Burn to Folder option for your project. Does that work?
If all you are trying to do is to use the PRE burning engine without any authoring you should give the completely free ImgBurn a try - it's pretty much the standard tool a lot of us use.
If though you want to use PRE to create your movie and then author it some more information would be helpful, especially concerning the camera, its shooting mode, how you got it into PRE, details of your computer and drivers ...
The following will help:
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Also, there are so many variables in the process you're describing that you're not really comparing apples to apples by any means.
There is no one way to create an AVCHD -- and an AVC file can have so many levels of compression and bit rate. So it's impossible to give a simple answer to why one program creates a 3 gig file and another program creates an 8 gig. It's because they're not the same file specs!
What are you burning your file to? What do you plan to use it for? What bit rate and compression rate are you using? Premiere Elements has over two dozen ways to output an H.264 video file.
You also don't say much about your computer specs, including what operating system you're using, if you are burning your outputs to your C drive or to a second drive, if all of your drives are formatted NTFS or if you regularly clear off junk files and defragment with a program like Advanced System Care Free. http://www.iobit.com/advancedsystemcareper.html
In fact, you haven't even told us about your source video (It's not 60p hi-def, is it?) or what settings you selected when you set up your Premiere Elements project.
This program will work and it will work well on a well-tuned system if you've got your project set up right and you're using optimized source footage.